Free Boundary Formulation for Boundary Value Problems on Semi-Infinite Intervals: An up to Date Review

Free Boundary Formulation for Boundary Value Problems on Semi-Infinite Intervals: An up to Date Review | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL Mathematical Methods in the Applied Sciences This is a preprint and has not been peer reviewed. Data may be preliminary. 5 January 2025 V1 Latest version Share on Free Boundary Formulation for Boundary Value Problems on Semi-Infinite Intervals: An up to Date Review Author : Riccardo Fazio 0000-0003-0825-0162 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.173607907.71021405/v1 Published Mathematical Methods in the Applied Sciences Version of record Peer review timeline 224 views 178 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract In this paper, we propose a review of the free boundary formulation for BVPs defined on semi-infinite intervals. The main idea and theorem are illustrated, for the reader convenience, by using a class of second-order BVPs. Moreover, we are able to show the effectiveness of the proposed approach using two examples where the exact solution both for the BVPs and their free boundary formulation are available. Then, we describe the free boundary formulation for a general class of BVPs governed by an n -order differential equation. In this context, we report three problems solved using the free boundary formulation. The reported numerical results, obtained by the iterative transformation method or Keller’s second-order finite difference method, are found to be in very good agreement with those available in the literature. The last result of this research is that, in order to orient the interested reader, we provide an extensive bibliography. Of course, we may aspect further and more interesting applications of the free boundary formulation in the future. Supplementary Material File (survey2024.pdf) Download 278.88 KB Information & Authors Information Version history V1 Version 1 05 January 2025 Peer review timeline Published Mathematical Methods in the Applied Sciences Version of Record 21 Oct 2025 Published Copyright This work is licensed under a Non Exclusive No Reuse License. Collection Mathematical Methods in the Applied Sciences Keywords bvps on infinite intervals free boundary formulation up to date review Authors Affiliations Riccardo Fazio 0000-0003-0825-0162 [email protected] Universita degli Studi di Messina View all articles by this author Metrics & Citations Metrics Article Usage 224 views 178 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Riccardo Fazio. Free Boundary Formulation for Boundary Value Problems on Semi-Infinite Intervals: An up to Date Review. Authorea . 05 January 2025. DOI: https://doi.org/10.22541/au.173607907.71021405/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . 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